With the rain coming down in sheets (blankets and pillow cases too) so as we spend the evening warm and cozy in our homes (surfing the Internet) Dr. J has brought out some pictures to show us, pictures of his laboratory. He is always looking for a chance to show off some of his experiments (at least those that are not deep dark secrets). Tonight we see the entry way, door or however it is Dr. J gets in, Figure 1. I figure the entry portal is there in the center - that light gray circle. Ah yes, and above are two new lights Dr. J just installed. It is quite dark when Dr. J first arrives, if he would just turn on those lights we could look around. Until he does, we can see some tubes or strange apparatus thingys on all sides. Looks like sparks emitting from each one. Watch your step in here!
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Figure 1. Dr. J's darkened laboratory.
Oh, that is better, the lights are on now. I can hardly wait to see what is off to the right. Those thingy things are very complicated. Rather pretty too. But where is Dr. J? He must be here somewhere, Figure 2. You do recall what he looks like, when he had that tan just before the storms?
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Figure 2. Dr. J shows off his new lights.
If you look closely you can see Dr. J just below the entry portal, in his white lab coat. There he is, his lab coat is spotless! It must be early in the evening to be so clean. Oh yes, he just arrived, Figure 3.
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Figure 3. Dr. J in his very clean lab coat.
Tonight's formula file not only uses exact tests to determine if pixels are in the cardioid or the circle, but also the rather difficult period 3 buds and small cardioid. These are components with orbits having period 1, 2 or 3. Pixels in these components are given special colors. Since the nature of these pixels is determined before iterations begin, the time consuming iterations otherwise used for these pixels is skipped. The pictures show the Mandelbrot set using the invert option, turning everything inside out relative to -.75. This is the boundary between the big cardioid and the big circle, which are transformed to the image top and bottom.
We shall be taking a closer look at some of the experiments in Dr. J's laboratory. So until then...
Stay warm,
Jay
frm:ColoritL { ; (c) Jay Hill, 1998
done = 1, z = 0, zc = 0, c = pixel
s=|c|, t1=(256*s - 96)*s + 32*Real(c), t2=16*s + 32*Real(c) + 16
B=sqrt(-4*c-7), t3=|8+4*c*(1-B)|, t4=|8+4*c*(1+B)| ; component tests
z=z + 249*(t1<=3) + 250*(t2<=1) + 251*(t3<=1) + 252*(t4<=1) ;
set colors
if(z>0) ; for periods 1, 2, and 3.
done=-1 ; color is set for c in a component, skip iterations
endif
: ; initialization.
zc=sqr(zc) + c ; standard MSet iteration
if (|zc| >= 4) ; Bailout at 4
done=-1 ; Set flag to force an exit.
endif
done >= 0 ; Continue if the flag >=0.
}
Dr_J_Lab_Lighting { ; (C) Jay Hill, 1998
reset=1960 type=formula formulafile=color101.par
formulaname=coloritl center-mag=-1.26603/-1.71058/0.5/1/90
float=y maxiter=256 inside=249 outside=summ
invert=1/-0.75/0 symmetry=xaxis periodicity=0
colors=000UcmFKcADU<6>24U02U02W<9>06\
j06l06n17p18q<3>19u2Aw4Bv<11>WYgZ_f`\
aecccddbee`<10>ssGttEuuCwwAwwAwvA<28\
>wdLwcMwcMwcM<90>wvuwvvwvvwwwwwvwwu<\
54>dd2ZF5KUAc0KwwcwwweeLLLC
savename=lablight
}
Dr_J_in_Lab_Coat { ; (C) Jay Hill, 1998
reset=1960 type=formula formulafile=color101.par
formulaname=coloritl center-mag=-1.73181/0/22/1/90 float=y
maxiter=256 inside=249 outside=summ invert=1/-0.75/0
symmetry=xaxis periodicity=0
colors=000UcmFKP<2>00L<16>06j06l06n1\
7p18q<3>19u2Aw4Bv<11>WYgZ_f`aecccddb\
ee`<10>ssGttEuuCwwAwwAwvA<28>wdLwcMw\
cMwcM<90>wvuwvvwvvwwwwwvwwu<54>dd2ZF\
5KUAc0KwwcwwweeLLLC
savename=labcoat
}
Dr_J_Lab_Darkened { ; (C) Jay Hill, 1998
reset=1960 type=formula formulafile=color101.par
formulaname=coloritl center-mag=-1.25/0/0.5/1/90
float=y maxiter=512 inside=249 outside=summ
invert=1/-0.75/0 symmetry=xaxis periodicity=0
colors=000UcmFKPADO57M<26>00U4Bv<11>\
WYgZ_f`aecccddbee`<10>ssGttEuuCwwAww\
AwvA<28>wdLwcMwcMwcM<90>wvuwvvwvvwww\
wwvwwu<54>dd2KA5AF5K0A000UUweeLLLC
savename=lab_dark
}
